Hello all! Glad to have found this helpful forum!
I’m starting my first bathroom remodel and have some questions as most of the information I find varies or is incomplete. I tried a quick search on the forum but didn’t find the exact information.

My questions :
What backer board should I use for the natural stone marble brick wall tile? Don’t feel i need cement board since it’s not a shower area - should I use green board or purple board? Marble tile will be pretty heavy and applied with thinset. The goal is to paint the half above the wall tile. Wasn’t sure if I should split cement board one half and drywall the other half up or keep existing drywall and cut out the bottom half with existing tile. Green board the whole room? Any help is appreciated!!!

Second question :

Since the existing floor is a mud job on top of a plywood sub floor I figured I would remove mud job down to plywood and build back up with plywood (if needed) and cement board for Marble hexagon floor tiles. I’m worried about subfloor movement I’ve been reading about - good idea or is there a better way?

The goal here is to do this job right the first time and not worry about things failing later on. Thank you in advance for your help!!!!

Regarding the walls, I would just use plain white sheetrock for all of it. I guess if you want to use the blue or purple for the top half it doesn't really matter, but since there's no tub or shower there, it doesn't seem necessary to do so.

While the walls will be supporting a good amount of weight, keep in mind that it's a sheer force pulling down on, not away from, the wall. I would just use screws every 8" and tile right over it.

Make sure to use an alkali-resistant mesh tape and thinset over any seams where there will be tile. The rest of it can get the standard paper tape and sheetrock mud.

For the floor, if done correctly, you've actually got the best setup there is for installing tile. A mud floor is hard to beat if it hasn't cracked and isn't crumbling. Removing the tile from it might be tough to do, but if it's solid and you can go over it, that's what I'd suggest.

Do you know how thick the mud bed is? Some of them were in the range of 2", which is a lot of plywood to build up.

What kind of tile is on the floor now? If it's not a natural stone, and you're planning to replace it with natural stone, then you get into whether or not the joist structure us up to par.